Solve for $x$ and $y$ using elimination. ${6x-3y = 39}$ ${5x+3y = 71}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3y$ and $3y$ cancel out. $11x = 110$ $\dfrac{11x}{{11}} = \dfrac{110}{{11}}$ ${x = 10}$ Now that you know ${x = 10}$ , plug it back into $\thinspace {6x-3y = 39}\thinspace$ to find $y$ ${6}{(10)}{ - 3y = 39}$ $60-3y = 39$ $60{-60} - 3y = 39{-60}$ $-3y = -21$ $\dfrac{-3y}{{-3}} = \dfrac{-21}{{-3}}$ ${y = 7}$ You can also plug ${x = 10}$ into $\thinspace {5x+3y = 71}\thinspace$ and get the same answer for $y$ : ${5}{(10)}{ + 3y = 71}$ ${y = 7}$